MEMS resonators are used in many military, biomedical and various end user applications. Accelerometers and gyroscopes, thermometers, and mass sensors with nanogram sensitivity are the most known applications that make use of resonator structures. In all of these applications, detection of the resonance frequency is crucially important. Moreover, when the quality factor is high, the small changes in resonance frequency are perceived more easily and the phase noise during close circuit oscillation gets lower.
MEMS resonators can simply be modeled with a spring, a mass and a damper (FIG. 1). When this system is actuated (driven) by a force, it moves. Maximum movement is observed when the actuation frequency is equal to the resonance frequency. In FIG. 2, a varying gap electrostatic MEMS resonator is illustrated. A typical electrostatic resonator comprises a drive electrode, a sense electrode and a DC polarization electrode.
If the movable proof mass that is polarized with DC voltage is actuated with AC drive voltage, it starts moving with the effect of electrostatic force (Electrostatic Drive). The gap changes because of the movement, leading to capacitance change that causes the generation of AC current at the sensing electrode. This current is defined as the output current.
The maximum output current is observed when the input voltage frequency is equal to the mechanical resonance frequency. The forces that are formed in varying gap resonators comprise different harmonic elements; however, the effect of higher harmonic components are not reflected into movement due to the band-pass structure of the resonator. As the relationship between the capacitance change and the change in the gap during the conversion of the motion into a current is not linear, the output current comprises other harmonic elements apart from drive frequency (main tone).
In the other studies in the literature, other harmonic elements in the output current have been neglected and only main tone has been used for the characterization of a resonator. However, the parasitic capacitance between the drive electrode and the sensing electrode (and the parasitic resistance formed in some cases) leads to the observation of parasitic currents in the main tone. The parasitic currents, that are also called feedthrough currents, may be limiting in some cases during the characterization of electrostatic MEMS resonators. Especially in applications requiring stiffer springs, as the voltage-current gain is reduced, the output current is dominated by the feedthrough current. For example in real-time measurements carried out in liquid mediums (fluid, gas etc.), the damping effect of the liquid(s) reduces the output whereas the fault currents may be more dominant.
While performing resonance characterization of a typical resonator, first, a frequency sweep is carried out when the electrostatic resonator is active. Following this, the DC bias of the resonator is turned off and another frequency sweep is carried out again at the same frequency ranges. The results of both characterizations can be subtracted from each other in a computer environment and the real resonance characteristics can be obtained. However, this method does not enable real-time characterization.
In order to enable real time resonance characterization, the feedthrough current should be eliminated from the system. Moreover, the closed loop oscillation is not possible without eliminating feedthrough current. To eliminate the feedthrough current, various methods have been proposed in the literature. In the first method, an active and a passive resonator are used. The passive and active resonators are driven with 180° phase different signals and thereby out-of-phase feedthrough currents are generated. When these currents are added at the sense electrode, ideally the feedthrough currents are eliminated. However, it is not possible to provide ideal elimination conditions. First, the phase difference between the generated signals needs to be exactly 180°. Moreover, the multiplication of the signal amplitudes and parasitic capacitances of the signals need to be as close to each other. When the two conditions are not completely satisfied, the feedthrough current cannot be completely eliminated. Another elimination method is a method where resonators with differential output currents are used. In this method, two out-of-phase currents of the same resonator is differentiated and mutual parasitic currents are eliminated. In the case that parasitic capacitances are mismatched, the signals obtained from the two outputs need to be multiplied by different gains and then they are subtracted from each other. If the gains of the signals are not properly adjusted, the feedthrough current cannot be completely eliminated. In addition, the differential method brings about an extra (application specific) resonator design cost.
The quality factor (Q) is an important parameter for accomplishing real time resonance characterization using the present methods based on the main tone signal. The high quality factor means that the gain at the resonance frequency is higher than gains in other frequencies. This makes it easier to detect the resonance frequency during open circuit resonance characterization and for closed loop oscillation. Especially the quality factors of resonators that operate in a fluid medium (liquid or gas) can be low because of the suppression of the output current by parasitic feedthrough currents due to the damping effect. In such applications, it may not always be possible to accomplish real time resonance characterization by using the present methods. Moreover, the quality factors of silicon MEMS resonators that operate under vacuum is limited by the quantum limit of silicon. According to this, There is a maximum value of the frequency-quality factor multiplication of the system (Q*f).
When the present applications of the known state of the art are taken into consideration, it can be seen that there exist no application having the same features of the proposed second harmonic reading based characterization/drive method that reduces the feedthrough current and increases the quality factor in electrostatic MEMS resonators. The reduction of the quality factor in high damping coefficient mediums and the repression of the resonator current due to the feedthrough current can be compensated by means of this invention.